Input Resistance of Common Gate question...

Hey all. I have been trying to calculate the input resistance of a common gate amplifier, but seem to have problems doing so.

I know I have to set a test voltage (or test current) at the input, and I've been told, to ground the output. So using the Hybrid pi model for a mosfet, I did the following to calculate the input resistance:

I apologize for my low quality picture. Please any help or hints are greatly appreciated. I just don't know what I am doing wrong. I have used the exact same technique on other amps and it seems to have worked fine, just not with common gates amps : (

What's the problem? You got the right answer. The input resistance of a common-gate amplifier goes to 1/gm as ro goes to infinity.

If you're trying to calculate it including Rd (which is not standard but sometimes done) then you forgot to include the current going from the VCCS to ground through Rd (equals Vo/Rd).

Thank you for your time and reply. Yes, I am trying to include Rd. If I take the node above the test voltage, there are 3 currents going in and out of that node. Rd doesn't seem to be part of any of those three. It also seems that Rd is shorted out due to connecting Vo to ground. How does one incorporate Rd into the equation?

Thank you for your time and reply. Yes, I am trying to include Rd. If I take the node above the test voltage, there are 3 currents going in and out of that node. Rd doesn't seem to be part of any of those three. It also seems that Rd is shorted out due to connecting Vo to ground. How does one incorporate Rd into the equation?

Once again thank you so much.

No problem. The issue is that Vo should be open; it is not shorted to ground. When you calculate the input resistance of a voltage amplifier you need to assume the output is connected to a high impedance. So your third current (that you set to zero) is wrong.

So the KCL equation should be ix = gmvx - vx/ro - (vx-vo)/ro

The second equation you need is vo = ixRl so you have (collecting terms)

ix + (ixRl)/ro = gmvx - vx/ro

Solving, rin = vx/ix = (1 + Rl/ro) / (gm+1/ro)

This is what you expect because if ro is larger than Rl (virtually always the case) then this collapses to 1/(gm+1/ro) ~= 1/gm